Question

These questions about number pattern is given to semester 1 grade 7 in my country and used as a standard curriculum.
Would you try?

1. Specify p = 1/3 + 1/9 + 1/27 + 1/81 + ....
2. Specify y = x + 13 + x + 23 + x + 33 + ... + x + 1003
3. 23a23b is divisible by 8 and 9. Specify a + b
4. If 0,201020102010 .... = x/y. Then the smallest number of x + y is
5.If this day is Tuesday, then 5^2000 day again is
6. Sandy celebrate her 25th anniversary on Friday. If during her lifetime, she spent 6 leap years, then Sandy was born on what day?

Answer 1

1- it goes by 1/3x we multiply the denominator by 3 each time

2- adding 10 to the denominator each time

6 - a leap year occurs every 4 years so she was born she witnessed 6 leap years
so there has been 6 day added in her entire life-time to her birthday
so Friday - 6 days = Saturday

5 - i have no clue how to do this
but i would say:
5^2000
5 represent Tuesday and 2000 represent the number of days
in those 2000 days there would be 166.67 years in those years there would be 41.67 leap years so we have 166.67 - 41.67 = 125 original years and 41.67 leaps years
lol so tricky i don't even know why i calculated those

Answer 2

1. let 3 being an x ,than your equation will be
1 1 1 1
p = --- + ----- + ----- + ----- + ......
x x^2 x^3 x^4

or

p = x^(-1) +x^(-2) +x^(-3) +x^(-4) + ...

2.

y = x+13 +x+23 +x+33+... +x+1003

let x+13 note an p so than your equation will be

y = p +p+10 + p +20 + .... + p+990

3. 23a23b divisible by 8 and 9 specify a+b

23^2(a*b)/(8*9)

23^2(8*9)/(8*9)

so a=8 and b=9 and a+b = 17

4.

will the second have not denominator there are sum of these x+13 and x+23

Answer 3

i actually quit
Ciao

Answer 4

@Will.H these above wrote is to you - that the second have not denominators

Answer 5

ciao to you to - are you Italian ? just bc. they say CIAO - or Saluti or Arrivederci

Answer 6

@jhonyy9 half Italian lol
good knowledge tho

Answer 7

cosi posso tio parlo italiano ma solo pocco perque i parlo piccolo ,ho laborato 7 anni a una firma taliano qui in hungaria

Answer 8

ma no lo so te capisi o no mio paroli - sorry

Answer 9

Oh my god
too close
well we both Europeans lol
but i was born in the states so i have limited ability in speaking Italian
is Hungarian the same! i think they share a few

Answer 10

not is problem - hope you understand me with my english too - so this is really true that your parents not learned you nothing from italian lenguage - or your grand parents not told to you in italian - or you dont visit never Italy ?

Answer 11

Been to Italy Rome several times. yeah my grandparents immigrated to USA and my parents did not care about Italian lol
but i was curious so i catche up a few words/ expressions and so

Answer 12

I think Kevin will hate us bc we keep spamming the question lol

Answer 13

hope so much that Kevin will can understanding that my subbmitt button again is blocked from where my past profile of champion was deleted - and again not was desblocked ,activated till today - Kevin sorry for this all - but hope so much that you remember about my blocked submitt button case -

Answer 14

Yup sorry Kevin for spamming lol

and jhonny you had another account?

Answer 15

yes past 4 or 5 years and in this year in month of may was deleted same with other to much profiles - hope you heard about these or you can reading about these on openstudyfeedback posted questions too -

Answer 16

Oh sorry to hear.

Your current account looks good tho high level and smart score

Answer 17

Hmm... sorry, but both of you have wrong answers. xD
Also for number 1 and 2, you must solve for p and y.

Answer 18

The first one is a G.P.

Answer 19

what is that?

Answer 20

The common ratio in the first question is 1/3.

Sum= \[\frac{a}{1-r}\]

Answer 21

G.P.=Geometric progression

Answer 22

Owh.. you mean geometric progression.
But, in 7th grade... the teacher still not teach them about geometric yet. You should solve it using number pattern

Answer 23

They don't know about arithmetic and geometric...

Answer 24

Well, forget that xD
You can solve it using geometric too actually. How about number 3-6?

Answer 25

What are the divisibility test for 8 and 9?

Answer 26

yup.. it's for number 3

Answer 27

Divisibility test for 8= a given number is divisible by 8 if the number formed by its last three digits is divisible by 8

Answer 28

A given number is divisible by 9 if sum of its digits is divisible by 9

Answer 29

Using 23b is divisible by 8,
then you'll find b = 2
Using (2 + 3 + a + 2 + 3 + 2) is divisible by 9,
-> (12 + a) is divisible by 9, then you'll find a = 6

Answer 30

jit mate a week ago you were at level 70 lol
moving fast

Answer 31

Yeah... that's it jitesh

Answer 32

how about number 4?

Answer 33

He was 79 before Will, I saw it xD

Answer 34

I mean 89

Answer 35

fair enough

Answer 36

Yes will u r also quicker

Answer 37

Not really lol

Answer 38

sorry for spamming again kevin

u 2 keep up

Answer 39

You too will...

Answer 40

Thx

Answer 41

Lol will

Let x=0.2010......

10000x=2010.2010.....
10000x=2010+x
9999x=2010

Answer 42

For number 1 :

p = 1/3 + 1/9 +1/27 + 1/81+ ....
p = 1/3 (1 + 1/3 + 1/9 + 1/27 ....)
p = 1/3 (1 + p)
p = 1/3 +1/3p
p - 1/3p = 1/3
2/3p = 1/3
p = 3/6 = 1/3

It's same for number 2
Maybe you'll get an idea for number 4-6 after seeing this...

Answer 43

Yeah.. that's true... lol
You are really awesome jitesh xD
Last question, how about question 5? Never mind question 6, it's same with question 5